I still don't have any solution to my problem. I've read some posts and look at some threads people have recommended but nothing seems to work for my phone. Both T Mobile and Samsung have refused to help me. so I'm still pretty much stuck without being able to use my OTG audio out feature when everyone else seems to be able to on their S4.

It was the obvious thing. The cable was defective. I just got two other cables from Amazon (very cheap). They both work perfectly immediately. The are both from different vendors, but they are both the exact same cable. They are different from the original in one way: the micro USB portion that plugs into the Galaxy S4 is much longer than the defective one. I don't know if that means anything, but there it is. Thanks to everyone for your help, especially DanBa who took extra time and effort to help me. Thanks!